Er,no . . . . or, . . .er, yes.
You can't close an account by simply clicking on a button somewhere. The main part of the site (i.e. ignoring Chatterbank) is intended to provide an ever-growing resource of information, so that people can search through old answers to find a solution to their problem. (Of course, it would help if the search facility ever actually worked properly!). So old posts aren't deleted. Accounts can be left unused but not actually be closed by the user.
However, the editor has the power to remove an account. (When that happens, all questions asked by the account holder, together with their answers to other questions, are wiped from the database). To get this to happen you need to send a begging letter to the editor, using the 'Contact Us' link at the foot of this page.
Chris